Ind. Eng. Chem. Res. 2001, 40, 3495-3501
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MATERIALS AND INTERFACES Kinetic Model of a Methacrylate-Based Monolith Polymerization Igor Mihelicˇ , Matjazˇ Krajnc, and Tine Koloini* Faculty of Chemistry and Chemical Technology, University of Ljubljana, Asˇ kercˇ eva 5, SI-1000 Ljubljana, Slovenia
Alesˇ Podgornik Bia Separations d.o.o., Teslova 30, SI-1000 Ljubljana, Slovenia
Monolithic stationary phases are becoming more and more important in the field of liquid chromatography, because they enable extremely fast separations. Methacrylate-based monoliths are produced via a free-radical bulk polymerization of glycidyl methacrylate and ethylene dimethacrylate using a benzoyl peroxide as an initiator. Preparation of large monoliths represents a big problem because of the heat release during the polymerization, which consequently leads to the distortion of the structure. A closer investigation of the polymerization, using differential scanning calorimetry, was performed in order to determine global kinetic parameters. A multiple heating rate method, based on the work of Ozawa, Flynn, and Wall, was applied for estimation of the values of the apparent activation energy, preexponential factor, and reaction order. Global polymerization kinetics is of first order with A ) 1.681 × 109 s-1 and Ea,app ) 81.5 kJ/mol, where the heat of polymerization is approximately 190 J/g. In addition, the influence of air and nitrogen atmosphere on polymerization is presented. Introduction Recently the field of chromatography has been characterized by a rapid development of many new stationary phases with improved characteristics. One of the main goals is to shorten the analysis time without changing the resolution power and binding capacity. Among different approaches, the so-called monoliths are promising candidates to fulfill these requirements.1 Apart from conventional stationary phases, made from a few micron porous particles, they consist of a single piece of porous material. The pores are open, forming a highly interconnected channel network which results in a fast mass transfer between the stationary and mobile phases.1 Another advantage of monoliths in comparison to the particulate stationary phases is their preparation.2 To obtain a uniform particle size distribution, a sieving process is required in the case of the particulate stationary phase, while the monoliths can be prepared in a defined shape already with a polymerization mould. Because of the above-mentioned advantages, they have been applied in various areas. Especially, methacrylatebased monoliths3 prepared in different shapes, from capillaries with a volume of a few microliters to the chromatographic columns for analytical purposes, were found to be suitable for extremely fast separations of large molecules.4-9 Furthermore, the methacrylatebased monolithic columns are also commercially available under the name convective interaction media (CIM).10 * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +386 1 24 19 530. Phone: +386 1 24 19 500.
However, the preparation of large, preparative monolithic columns still represents a big challenge. Very few attempts have been described so far11,12 and only recently has an approach demonstrating chromatographic characteristics of large monolithic columns been introduced.13 The main reason lies in the extremely difficult preparation of a large monolith with a uniform structure over the entire volume. The structure of the monolith is highly dependent on the temperature increase in the mould during the polymerization.12 The polymerization is highly exothermic; however, to keep the temperature in the mould inside the allowed temperature interval, a method for heat removal must be applied. Therefore, the moulds are placed into a thermostated water bath. In the case of small-diameter moulds, the temperature profile can be kept fairly flat in the radial direction and unchanged during the polymerization.12 In the case of large-diameter moulds, the conductive heat transfer inside the mould represents a significant resistance to heat transfer that causes the accumulation of heat and consequential large temperature differences in the radial direction. This effect manifests in the morphology of the monolith as a nonhomogeneous structure.12 The possibilities of controlling the bulk polymerization are very limited in this case; therefore, the temperature increase is determined already by starting experimental conditions. These conditions are composition of the reactant mixture, temperature of the water bath, diameter of the mould, shape and thermal conductivity of the mould, and heat-transfer coefficients on both sides of the mould. A prerequisite for a successful setting of experimental conditions is detailed knowledge about polymerization kinetics and heat transfer, which en-
10.1021/ie010146m CCC: $20.00 © 2001 American Chemical Society Published on Web 07/14/2001
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ables in combination with an appropriate mathematical model, the prediction of the temperature profiles during polymerization. Because our interest is focused mainly on the heat balance, a detailed mechanism of radical copolymerization is not necessary, but rather the estimation of the overall kinetics and the generated heat of polymerization, which are required in the mathematical model, is necessary. The purpose of this work was to study the overall kinetics of the copolymerization and to determine the heat of reaction. Additionally, the influence of air and nitrogen atmosphere on the polymerization is presented. Materials and Methods A polymerization mixture consists of two monomers, 24% glycidyl methacrylate and 16% ethylene dimethacrylate, both from Aldrich (Steinheim, Germany), and inert porogens (12% dodecanol and 48% cyclohexanol) and an initiator (benzoyl peroxide, BPO), all from Fluka (Buchs, Switzerland).12,14 This mixture forms a clear liquid that polymerizes via a free-radical mechanism using an initiator. Polymerization results in a two-phase system, a white-colored continuous solid monolith and inert liquid porogens inside the porous structure of the monolith. In some experiments a mixture comprised only of monomers was used. Such a mixture is further on in the text considered as a monomer mixture, and similarly the mixture of two porogens is referred to as porogen mixture. Generated heat of the thermally initiated polymerization was measured by using differential scanning calorimetry (DSC) on a Mettler Toledo 821c differential scanning calorimeter at constant atmospheric pressure in nitrogen and air atmosphere. Dynamic scans were taken at heating rates of 2, 5, 10, 15, and 20 °C/min, respectively, in a temperature range of 40-170 °C. For a DSC sample preparation, approximately 10 mg of the mixture was filled into an aluminum crucible of 40 µL with a perforated lid. The weight of the samples was measured accurately by differential weighing using a microbalance. The heat flow data and the area under the thermogram obtained from the DSC were processed to obtain the required information. Results and Discussion Kinetic parameters of the polymerization were determined by using DSC, which is often applied for solving kinetic problems due to a simple and fast sample preparation and measurements in a wide range of experimental conditions.15 The study of reaction kinetics with the use of DSC assumes that the amount of the generated heat caused by the reaction is directly proportional to the extent of reaction x of the sample at a given time (t) and then relates the rate (dx/dt) to the rate of the generated heat. Several different methods enable derivation of the global kinetic equation from DSC experiments, such as the isothermal method, single-heating rate method, multiple-heating rate method, and time-temperature superposition method.16 The isothermal method is highly recommended for characterization and modeling of polymerizations because of its effectness in distinguishing between different reaction types and accuracy. However, in the studied polymerization system, this method was not suitable because two contrary thermic effects are present. One is exothermic polymerization of monomers and the other
endothermic evaporation of porogens. Because of the pronounced negative heat flux caused by the evaporation, no reasonable setting of the baseline was possible. For this reason, the multiple-heating rate method, based on the work of Ozawa17 and Flynn and Wall,18,19 was applied. Using this method, it is possible to estimate kinetic information for systems with multiple reactions, irresolvable baselines, and residual solvent without the knowledge of the reaction mechanism.20,21 The multipleheating rate method has been empirically proved to be an isoconversional technique22 for several systems. It allows the estimation of the polymerization kinetics from the relationship between the heating rate (β ) {dT}/{dt}) and the isoconversional temperature, which is the temperature at maximal heat flow (Ti). This method is valid for systems where the preexponential factor, the activation energy, and f(x) are independent of the temperature. The kinetic equation in terms of the extent of reaction can be written as
dx ) f(x) A exp[-Ea,app/RT], f(x) ) (1 - x)n (1) dt where x stands for the extent of reaction. Assuming an overall first-order reaction kinetic, the plot of log β vs Ti-1 should be linear and can be described by the equation
log β ) aTi-1 + b
(2)
where the slope (a) and the intercept (b) are defined as
a ) -0.4567Ea,app/R
(3)
b ) -2.315 + log(AEa,app/R)
(4)
Therefore, the apparent activation energy can be calculated as follows:
Ea,app ) -2.19R
d log β dTi-1
(5)
Figure 1 presents the DSC thermograms of the polymerization mixture (for the composition, see the Materials and Methods section). The DSC thermograms first reach the maximum of the heat flow, which is caused by an exothermic radical polymerization of monomers, followed by a steep decline of the heat flow. This effect represents the evaporation of porogens from the mixture. Because two contrary effects simultaneously take place in the process of the polymerization, the data from Figure 1 cannot as such be used for the calculation of kinetics by the Ozawa-Flynn-Wall method, because the evaporation process could shift the temperature of the maximal heat flow. To perform the required calculation of the kinetics, both effects, endothermic evaporation of porogens and exothermic polymerization of monomers, should be separated. Therefore, DSC evaporation thermograms of porogens at different heating rates and DSC evaporation thermograms of the mixture of porogens and monomers without an initiator were measured separately. DSC thermograms presenting the evaporation of porogens and the mixture of porogens and monomers overlap quite well up to 110 °C (Figure 2). This indicates that the presence of monomers in the solution does not effect the evaporation of porogens. At higher temperatures, a large difference between both samples occurs,
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Figure 1. Normalized DSC thermograms presenting radical polymerization of the mixture at different heating rates. Composition of the samples: 12% dodecanol, 48% cyclohexanol, 24% glycidyl methacrylate, 16% ethylene dimethacrylate, and an initiator. Nitrogen atmosphere.
Figure 2. DSC thermograms presenting the evaporation of the porogens and the mixture of porogens and monomers at different heating rates. Composition of porogens: 20% dodecanol and 80% cyclohexanol. Composition of the mixture of porogens and monomers: 12% dodecanol, 48% cyclohexanol, 24% glycidyl methacrylate, and 16% ethylene dimethacrylate. Nitrogen atmosphere.
which may be attributed to a spontaneous thermally initiated polymerization of the sample containing monomers. Consequently, the effect is expressed in higher values of the normalized heat flow because of its exothermic nature. This assumption was confirmed by DSC experiments where the heat flow of the monomer mixture without an initiator and porogens was measured. The results are presented in Figure 3. It clearly confirms that thermally initiated polymerization of monomers without an initiator really occurs at high temperatures. With the numerical addition of the DSC thermograms presenting the evaporation of porogens (Figure 2) and the DSC thermograms presenting the polymerization
of the mixture (Figure 1), the exothermic effect of the polymerization can be isolated. The mathematical procedure of the addition of DSC thermograms is shown graphically in the inserted diagram of Figure 4. Using this simple procedure, DSC thermograms presenting only the exothermic effect of the polymerization for all heating rates were calculated. The results are shown in Figure 4. By the comparison of isoconversional temperatures from Figures 1 and 4, it can be seen that the evaporation process during the polymerization does not significantly shift the positions of the peak maximum, which are required for the kinetic calculation. From the thermograms presented in Figure 4, the
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Figure 3. DSC thermograms presenting thermally initiated polymerization of monomers at different heating rates. Composition of the samples: 60% glycidyl methacrylate and 40% ethylene dimethacrylate. Nitrogen atmosphere.
Figure 4. Calculated DSC thermograms of the polymerization mixture derived from the numerical addition of porogen evaporation DSC thermograms (Figure 2) and the polymerization mixture DSC thermograms (Figure 1). The calculation procedure is graphically presented as an inset.
reliable data needed for the estimation of kinetic parameters by the Ozawa-Flynn-Wall method can be extracted. By drawing the data (Figure 5) and fitting them with the linear function (eq 2), we obtain a linear dependence of log β vs Ti-1, which confirms the overall first-order reaction. Using eq 3 with a known slope of the linear fit, the preexponential factor can be calculated, and it is equal to 1.681 × 109 s-1. The apparent activation energy can be calculated through the application of the intercept of the linear fit in eq 5, which results in 81.5
kJ/mol. These values are comparable to other experimental values for similar methacrylate polymerizations.23,24 The heat of reaction is an important parameter for the estimation of the temperature increase and for the determination of the steric hindrance during the polymerization. Because the porogens are not involved in the polymerization process, the comparison of the heat of reaction with the same ratio of monomers is justified. The calculation of the heat of reaction from normalized DSC polymerization thermograms is rather simple.
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Figure 5. Dependence of the logarithm of the heating rate versus the inverse value of the isoconversional temperature. The straight line represents the linear fit of the points; fitted parameters and errors are given in the inset.
Figure 6. DSC thermograms present the polymerization of the monomer mixture at different heating rates. Composition of the samples: 60% glycidyl methacrylate, 40% ethylene dimethacrylate, and an initiator. Nitrogen atmosphere. The inset shows the procedure of the baseline setting and the numerical integration using the exothermic peak at 10 K/min.
By adoption of eq 6 and performance of the numerical integration of exothermic peaks, the solution for the heat of polymerization is straightforward.
∆Hr [J/g] )
∫ABm1
dHr dt dt
(6)
DSC thermograms presenting the polymerization of monomers in nitrogen atmosphere are shown in Figure 6. Based on the assumption the heat capacity difference
between reactants and products is very small, a linear baseline is drawn between the points A and B, used as the lower and upper limits in the integration procedure. The inserted thermogram in Figure 6 shows a typical procedure of the calculation of the heat of polymerization including the baseline setting and the numerical integration. Original values of the normalized heat of polymerization cannot be directly compared, because the mixture consists of only 40% monomers. To enable a direct comparison of the values of the normalized heat
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Figure 7. Comparison of DSC thermograms presenting the polymerization of the monomer mixture under nitrogen and air atmosphere at different heating rates. Composition of the samples: 60% glycidyl methacrylate, 40% ethylene dimethacrylate, and an initiator. The inset shows the detail of the pronounced heat flow at high temperatures, which is characteristic for the polymerization in air atmosphere.
of polymerization for monomers in J/g(monomers) with the values for the polymerization mixture in J/g(mixture), they were multiplied by the proportion of monomers in the sample. The difference between both heats of polymerization is negligible because the values are scattered in a 190 J/g ( 5% interval. This is mostly due to baseline setting problems and the error of the numerical integration of the thermograms. A negligible difference between both heats of reaction is reliable evidence that porogens do not take part in the polymerization and that no major steric hindrance effects are present. Oxygen can be a powerful inhibitor in radical polymerizations. It reacts with radicals to form relatively unreactive peroxy radicals that react with themselves or with another propagating radical by coupling or by disproportionation reactions and to form inactive products. However, the action of oxygen is anomalous, in that it is known to initiate some polymerizations. The initiation probably occurs by the thermal decomposition of peroxides and hydroperoxides formed from the monomer. Whether oxygen is an inhibitor or an initiator, it will be highly temperature dependent. The initiation will occur at high temperatures where peroxides and hydroperoxides are unstable. These effects are presented in Figure 7, which shows the comparison of the DSC thermograms of the polymerization of monomers under nitrogen and air atmosphere, respectively. A delay in the start of the polymerization at low temperatures in the presence of air indicates the inhibition caused by the oxygen on the one hand. While, on the other hand, the magnified part of Figure 7 presents the initiation of residual monomers at high temperatures, where peroxides and hydroperoxides decompose.25-27 Conclusions The global kinetics of the methacrylate-based monoliths polymerization was determined using DSC. An
isoconversional multiple-heating rate method for the determination of the kinetic parameters was applied. With the results obtained, it is possible to model the polymerization process in terms of the temperature distribution for different shapes and sizes of the moulds at different experimental conditions, which is of great importance for the construction of large-volume methacrylate-based monoliths with a uniform structure. Acknowledgment We acknowledge the Ministry of Science and Technology of Republic of Slovenia for support of this work through Project Nos. L2-1522-0158-99 and PS-103-510. Symbols a ) slope of the linear equation (eq 2) A ) preexponential factor [s-1] b ) intercept of the linear equation (eq 2) β ) heating rate [K/min] T ) temperature [K] Ti ) isoconversional temperature [K] t ) time [s] m ) mass [g] ∆Hr ) heat of reaction [J/g] Ea,app ) apparent activation energy [J/mol] n ) order of the reaction x ) extent of the reaction R ) gas constant [J/mol‚K]
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Received for review February 13, 2001 Revised manuscript received May 14, 2001 Accepted May 30, 2001 IE010146M
